Pearson Edexcel Level 3 Advanced Subsidiary and Advanced ...

[Pages:32]Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Statistics

Statistical formulae and tables

For first certification from June 2018 for: Advanced Subsidiary GCE in Statistics (8ST0)

For first certification from June 2019 for: Advanced GCE in Statistics (9ST0)

This copy is the property of Pearson. It is not to be removed from the examination room or marked in any way.

P58394A

?2017 Pearson Education Ltd. 1/1/1/1/1/1/1/

Edexcel, BTEC and LCCI qualifications Edexcel, BTEC and LCCI qualifications are awarded by Pearson, the UK's largest awarding body offering academic and vocational qualifications that are globally recognised and benchmarked. For further information, please visit our qualification website at qualifications.. Alternatively, you can get in touch with us using the details on our contact us page at qualifications.contactus About Pearson Pearson is the world's leading learning company, with 35,000 employees in more than 70 countries working to help people of all ages to make measurable progress in their lives through learning. We put the learner at the centre of everything we do, because wherever learning flourishes, so do people. Find out more about how we can help you and your learners at qualifications.

All information in this document is correct at time of publication. ISBN 978 1 4469 4764 7 All the material in this publication is copyright ? Pearson Education Limited 2017

Contents

1 Introduction

1

2 AS Level in Statistics

2

3 A Level in Statistics

4

4 Statistical Tables

8

Table 1: Cumulative Binomial Distribution Function

8

Table 2: Cumulative Poisson Distribution Function

15

Table 3: Normal Distribution Function

17

Table 4: Percentage Points of the Normal Distribution

18

Table 5: Percentage Points of the Student's t-distribution

19

Table 6: Percentage Points of the 2 Distribution

20

Table 7: Percentage Points of the F-distribution

21

Table 8: Critical Values of the Product Moment Correlation Coefficient

23

Table 9: Critical Values of Spearman's Rank Correlation Coefficient

24

Table 10: Critical Values of the Wilcoxon Signed-Rank Statistic

25

Table 11: Critical Values of the Wilcoxon Rank-Sum

26

1 Introduction

The formulae in this booklet have been arranged by qualification. Students sitting AS Statistics papers should refer to Section 2, pages 2 ? 3. Students sitting A Level Statistics papers should refer to Section 3, pages 4 ? 7.

Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Statistics

1

Statistical Formulae and Tables ? Issue 1 ? August 2017 ? ? Pearson Education Limited 2017

2 AS Level in Statistics

Population variance, 2, =

x2

N

-

2

=

1 N

(

x

-

)2

Population standard deviation, , =

x2

N - 2 =

1 N

(x

-

)2

Sample variance =

( ) n

1 -

1

x2

-

x

n

2

=

n

1 -

1

(

x

-

x )2

Sample standard deviation =

( ) n

1 -

1

x2

-

x

2

n

=

n

1 -

1(x

-

x )2

Binomial probability calculations:

P(X

=

x) =

n x

px (1 -

)p n - x

Mean = np

Variance = np(1 - p)

For a random sample of nx observations from N(, 2 )

X

-

~

NN((00, ,11) )

n

Test statistic for a binomial proportion using normal distribution:

p^ - p

p(1 - p)

~ NN((00,,11))

n

2

Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Statistics

Statistical Formulae and Tables ? Issue 1 ? August 2017 ? ? Pearson Education Limited 2017

Product moment correlation coefficient:

r=

S xy

=

(xi - x )( yi - y)

=

{ }{ } Sxx ? Syy

( xi

-

)2

x

( yi

-

)2

y

xi yi

-

(

xi )(

n

)yi

( ) ( )

xi2 -

xi

2

n

yi2 -

yi

2

n

Coefficients for least squares regression line: least squares regression line of y on x is y=a+bx , where a = y - bx

( )( ) the regression coefficient of y on x is b = Sxy = ( ) Sxx

xi - x yi - y xi - x 2

Test for association:

( ) Oi - Ei 2 is approximately distributed as 2

Ei

Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Statistics

3

Statistical Formulae and Tables ? Issue 1 ? August 2017 ? ? Pearson Education Limited 2017

3 A Level in Statistics

Population variance, 2, =

x2

N

-

2

=

1 N

(

x

-

)2

Population standard deviation, , =

x2

N - 2 =

1 N

(x

-

)2

Sample variance, s2, =

( ) n

1 -

1

x2

-

x

n

2

=

n

1 -

1

(

x

-

x )2

Sample standard deviation, s, =

( ) n

1 -

1

x2

-

x

2

n

=

n

1 -

1(x

-

x )2

Binomial probability calculations:

P(X

=

x) =

n x

px (1 -

)p n - x

Binomial mean = np

Binomial variance = np(1 - p)

For a random sample of nx observations from N(, 2 )

X

-

~

NN((00, ,11))

n

Test statistic for a binomial proportion using normal distribution:

p^ - p

p(1 - p)

~ NN(0(0, ,11))

n

4

Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Statistics

Statistical Formulae and Tables ? Issue 1 ? August 2017 ? ? Pearson Education Limited 2017

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